The District of Columbia's acting chief medical examiner announced yesterday that he does not want to continue running the medical examiner's office, and sources said his decision resulted from an argument with city officials about budget cutbacks.

Douglas Dixon, who took over as acting chief medical examiner in May, said yesterday that he wants to stay as a deputy medical examiner, but that on Wednesday he told his boss, Commissioner of Public Health Dr. Ernest Hardaway, that he wanted "to be relieved of responsibility" for the acting chief's job.

Hardaway said Dixon told him he wanted to be removed from the chief's job earlier this week after the two argued about a number of matters, including vacation time for a departing employe.

But one source familiar with the office said Hardaway had "accused Dixon of not doing his job and not fulfilling his responsibilities." Another source said the two argued about Hardaway's contention that Dixon and his predecessor, Dr. James Luke, inadvertently stalled filling vacant positions by not preparing the paper work required under the city's personnel policies.

Sources familiar with the operation of the office agree that Dixon left the chief's job for the same reasons that Luke, the city's chief medical examiner for the last 12 years, resigned in May--budget cutbacks in the office and critical shortages in staff.

"These individuals over there in the medical examiner's office are holding the city hostage," Hardaway said. "They keep playing with the media."

Law enforcement officials have expressed concern that the D.C. medical examiner's office, for years considered one of the nation's best, is in danger of becoming a second-rate operation, and several officials said yesterday that they see Dixon's decision as another step in that process.

"I'm very apprehensive," said Steve Gordon, chief of the felony division of the U.S. attorney's office here. "I don't know what happens now . . . . Dixon's been breaking his back for months. He worked real, real hard to hold that place together."

"This is a very serious matter from the standpoint of our office," added U.S. Attorney Stanley S. Harris.

Officials of the office have expressed the fear that the prosecution of some homicide cases could be hampered. They say they believe that medical examiners and technicians are so overworked they could mistake a murder for a natural death, or could perform sloppy autopsies that could lead to acquittals.

"I'm concerned that we maintain the quality of the medical examiner's office," said D.C. Police Chief Maurice T. Turner Jr., asked to comment on Dixon's resignation. "That office is essential in the investigation of deaths in the city."

In recent months Dixon has argued repeatedly with Hardaway about the need to hire forensic pathologists to fill the positions of those who have left, according to Hardaway and knowledgeable sources.

The office started the year with six doctors, but is now down to three, with the prearranged resignation of Dr. Stuart Dawson earlier this week.

The office had 41 staff positions two years ago, but has only 30 staff members now, sources said. Hardaway has said recently that he was expediting the hiring of five autopsy technicians, who transport bodies and help prepare for autopsies.

Hardaway said he is seeking advice from people outside government on finding a chief medical examiner.